SOLUTION: There are x chickens and y rabbits on a farm. Given that the animals have a total of 70 heads and 196 legs, formulate a pair of simultaneous equations involving x and y. By solving
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Question 1160221: There are x chickens and y rabbits on a farm. Given that the animals have a total of 70 heads and 196 legs, formulate a pair of simultaneous equations involving x and y. By solving the simultaneous equations, find the number of chickens and rabbits on the farm.
Found 3 solutions by Theo, josgarithmetic, solver91311:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
chickens have 2 legs.
rabbits have 4.
chickens and rabbits have 1 head each.
let x = the number of chickens.
let y = the number of rabbits.
x + y = 70 is the equation for the total number of heads.
2x + 4y = 196 is the equation for the total number of legs.
these 2 equations need to be solved simultaneously to find out how many chickens and how many rabbits.
multiply both sides of the first equation by 2 and leave the second equation as is to get:
2x + 2y = 140
2x + 4y = 196
subtract the first equation from the second to get:
2y = 56
solve for y to get:
y = 56/2 = 28
since x + y = 70, then x must be equal to 70 - 28 = 42
you have 42 chickens and 28 rabbits.
they each have 1 head, so x + y = 70 becomes 42 + 28 = 70 which is confirmed to be correct.
each chicken has 2 legs and each rabbit has 4 legs, so 2x + 4y = 196 becomes 42 * 2 + 28 * 4 = 84 + 112 = 196 is also confirmed to be correct.
your solution is that there are 42 chickens and 28 rabbits on the farm.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
2 legs per chicken
4 legs per rabbit
Simplify the legs equation.
Eliminate x, to,...
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
and, presuming that all of the chickens have two legs and all of the rabbits have four legs:
Solve the 2X2 system for 
and 
John
My calculator said it, I believe it, that settles it
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